Simplify the following expression: $y = \dfrac{r^2 - 7r + 12}{r - 3} $
First factor the polynomial in the numerator. $ r^2 - 7r + 12 = (r - 3)(r - 4) $ So we can rewrite the expression as: $y = \dfrac{(r - 3)(r - 4)}{r - 3} $ We can divide the numerator and denominator by $(r - 3)$ on condition that $r \neq 3$ Therefore $y = r - 4; r \neq 3$